Photonic crystals are formed from materials with a dielectric constant that varies periodically in one, two or three spatial dimensions. This periodicity gives rise to the appearance of frequency bands in which signal propagation is not permitted inside the crystal. These forbidden frequency bands are commonly known as the Photonic Band Gap (PBG). Light propagation can be controlled by inserting defects that alter the periodicity of the crystal. The insertion of linear defects leads to the appearance of guided modes at frequencies within the forbidden band allowing the propagation of light only in the defect created. Although total control of the propagation of light is achieved by using 3D photonic crystals, control of light in three dimensions can also be achieved with planar 2D photonic crystals, thus reducing the cost and complexity of manufacture. In this case, the light is confined to the direction perpendicular to the plane of the crystal if the dielectric constant of the materials above and below the crystal is less than the dielectric constant of the defect created in the crystal. The main advantages of the devices based on photonic crystals are a considerable reduction in size, allowing highly integrated optical circuits to be produced, and the possibility of implementing curved guides with radii of the order of the wavelength of the signal that is being propagated without significant losses, which is essential for the development of microphotonics.
Due to the scaling properties of Maxwell's equations, photonic crystals can be made to have a forbidden band in any spectral range provided the structure is appropriately scaled and provided materials are chosen that have suitable properties in the chosen spectral range. As it is extremely costly to manufacture structures in the visible or infrared frequencies, in which the spatial periodicity should be less than one micron, photonic crystals have been implemented to work at microwave frequencies where the periodicity is of the order of cm. To do this, bars of dielectric material with a high refraction index are used that form periodic lattices in air. The properties of these structures can by and large be extrapolated to the structures corresponding to optical frequencies, but with the advantage that at microwave frequencies, manufacture and measurement of the properties is much easier.
In a photonic crystal, a waveguide can be created from a chain of equally spaced cavities or point defects along a certain direction of the crystal. This type of guide is known as a coupled cavity waveguide. The propagation along these guides is explained by photons jumping between adjacent cavities due to overlap of the evanescent field tails. The coupled cavity waveguides have certain characteristics that make them particularly interesting: on the one hand, a theoretical expression can be derived for the dispersion ratio of the guide modes from a tight-binding approach used in solid-state physics. On the other hand, transmission along curves with very tightly curved radii is very efficient provided that symmetry of the cavity mode is appropriate. In addition, the group velocity of this type of guide is very low, tending to zero at the edges of the band, and so highly efficient non-linear processes are expected in this type of guide, as well as high dispersion that could be of use in a number of applications.
On the other hand, couplers in photonic crystal technology can be implemented in the same way as used by other more mature technologies, such as integrated guides or fiber optics: disposing two parallel wave guides close to one another. If both guides are identical and single moded when placed in proximity, the two interact and the guide mode of an isolated guide divides into two modes for the complete system of the two parallel waveguides. These modes have even and odd symmetry with respect to the plane equidistant from the guide axis. In addition, these modes have different propagation constants, implying that they travel at a different velocity along the coupler. This behavior causes a signal to be excited in one of the two guides, after a certain distance the wave passes to the adjacent guide and, once again, returns to the original guide after covering the same distance. That is, there is a periodic transfer of power between guides. In 2D photonic crystals, couplers have been proposed and studied formed from guides made by completely eliminating a row of cylinders in dielectric cylinder structures over air. The performance of a directional coupler has also been shown experimentally at optical frequencies in a planar photonic crystal with air holes on a silicon substrate. In addition, a coupler has been proposed in a 2D photonic crystal of air holes in dielectric for commutation applications.
The power dividers/combiners are fundamental blocks in any optical network or device. Their function is to distribute the power of an input signal to two output ports with certain percentages at each output. If the percentages are 50%, the divider is usually called a 3 dB divider. These blocks can be implemented mainly in two ways (see FIGS. 1a and 1b): either using a directional coupler designed such that the power is divided equally between the output ports at on output (FIG. 1a), or by means of a Y-shaped structure in which the input guide divides into two output guides at a certain angle to minimize losses (FIG. 1b).
For the first case, the phase difference between the output signals is 90% whereas for the second case, both outputs are in phase. In addition to couplers, the implementation of Y-shaped dividers has also been proposed in photonic crystal technology and it has been demonstrated experimentally at both microwave and optical frequencies.